by Andrew G. Bell
abell118@ivytech.edu
(260) 481-2288
Chapter 17
Capacitance
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Capacitor
• An electrical component consisting of
two conductors (plates) separated by an
insulator (dielectric)
• A component that opposes a change in
circuit voltage
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Dielectric Materials
Vacuum
Air
Paper
Plastic
Glass
Ceramic
Aluminum Oxide
Tantalum Oxide
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Electrical Definition of Capacitor
• An electrical component that stores
energy in the form of electrical charge
when voltage is applied
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Basic Symbols
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Capacitor Action
• Applied voltage forces electrons onto
one plate. The electrostatic field
associated with a charged particle
forces electrons off of the opposite
plate.
kQ1  Q2
F
2
d
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Capacitor Charging
• Applied voltage causes circuit current to
flow. Plates of the capacitor become
charged as one plate accumulates
electrons and the other releases
electrons. Circuit action continues until:
VC = VS
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Capacitor Discharge
• A charged capacitor will discharge when
a path is provided between the two
plates.
• The plate with excess electrons will give
up electrons to the plate with a
deficiency until:
VC = 0 V
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The Farad
• Capacitance is the capacity of a
capacitor to store electrical charge.
• The unit of measure is the farad (f).
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Charge and Voltage
Q
C
V
Q  C V
Q
V
C
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Energy Stored in Field
CV 2
Energy 
2
Energy = joules stored
C = capacitance (farads)
V = voltage
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Factors and Value
ITEM
Plate area
Plate distance
Dielectric material
RELATIONSHIP
Direct
Inverse
Direct
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Dielectric Constant
0
k
v
0: Absolute permittivity of dielectric
materials
v: Absolute permittivity of vacuum
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Dielectric Types
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Dielectric Strength
• The breakdown voltage rating of a given
material and dimensions
• Dielectric material reaches point where
punch-through occurs
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Capacitor Formula
8.85 A
C
12
10 s
Use Excel to evaluate how Area,
Spacing and dielectric constant
change the capacitance of a
parallel plate capacitor
C = capacitance (farads)
A = area of plates (sq. meters)
s = spacing between plates (meters)
8.85 = constant for air/vacuum
Excel
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Finding Total Capacitance
• For series capacitors:
– Sum of the reciprocals
1
CT 
1
1
1
1


 
C1 C2 C3
Cn
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Finding Total Capacitance (cont.)
• For two series capacitors:
– Product-over-the-sum
C1  C2
CT 
C1  C2
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Finding Total Capacitance (cont.)
• For parallel capacitors:
– Direct summation
CT  C1  C2    Cn
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Total Capacitance
C1
10µF
Using Excel calculate the
total capacitance of each
circuit
C2
22µF
CT
C3
47µF
Excel
C1
10µF
C2
22µF
C3
47µF
CT
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Series Voltage Distribution
CT
VX  VS
CX
VX = voltage across capacitor x
VS = DC source voltage
CT = total series capacitance
CX = value of capacitor x
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Example
Use Multisim
determine the
voltage across
each capacitor
Multisim
Multisim
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Charge Distribution
• In parallel circuits: Q  C V
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RC Time Constant ()
• Time required for a capacitor to charge
or discharge 63.2% of the change in
voltage level applied
• Five time constants are needed to fully
charge/discharge
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Time Constant Chart
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R=
1.0E+3 ohms
C = 47.0E-6 farad
 = 47.0E-3 seconds
5 = 235.0E-3 seconds
pulse width = 235.0E-3 seconds
period = 470.0E-3 seconds
Assuming a 9V
Square wave input
Use Multisim and
Excel to determine
the RC Time
Constant and plot
the transient
response
Excel
Multisim
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Exponential Form
for Charging Capacitors

v R  VS  
t

 = epsilon (or 2.71828)
t = time allowed (seconds)
 = R × C (or 1 time constant)
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Exponential Form
for Discharging Capacitors

vR  VS 1  


t




 = epsilon (or 2.71828)
t = time allowed (seconds)
 = R × C (or 1 time constant)
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Capacitor Types
FIXED
Paper/Plastic
Mica
Ceramic
Electrolytic
Chip
VARIABLE
Trimmer
Air
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Ratings
•
•
•
•
•
•
Temperature
Tolerance
Voltage Rating
Temperature Coefficient
Power Factor
Inductance Characteristics (at high
frequencies)
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Safety
• Always discharge circuit capacitors after
power has been removed and before
working on circuits containing them.
• Observe polarity when connecting
electrolytic capacitors into a circuit.
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Ratings
•
•
•
•
•
•
•
Physical Size and Mounting
Capacitance Value
Capacitance Tolerance
Working Voltage Ratings
Temperature Range
Temperature Coefficient
Inductance
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Typical Problems
Ohmmeter Tests
Opens
Shorts
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